No, they’re not the same thing.
Training means breaking down the skill into it’s constituent parts, strengthening what is weak and further fortifying what is already strong. Practicing means performing the skill in it’s entirety and adjusting to the feedback you receive. Play is experimentation, exploration and improvisation that stretches the boundaries of your ability.
You need all three.
But to do them consistently, to show up every day and do the work, requires discipline. In the beginning, skill can be acquired without much discipline. But if you wish to accelerate your ability and become really good at what you do, you can’t do it without discipline.
Discipline is what gets you through the plateaus. Discipline is what helps you show up when your world is crumbling. Discipline is what makes it possible to endure through the trials and the twists and the turns.
My rule for writing is this: Every day. For decades. It applies to any skill. To show up, every day, for decades, requires several things. One of which is discipline. So perhaps a new heuristic concerning skill acquisition:
No great ability without great discipline.